Jamieson, Fausset and Brown on 1 Corinthians 7:15

15. if ... depart--that is, wishes for separation. Translate, "separateth himself": offended with her Christianity, and refusing to live with her unless she renounce it.

brother or a sister is not under bondage--is not bound to renounce the faith for the sake of retaining her unbelieving husband [Hammond]. So De 13:6; Mt 10:35-37; Lu 14:26. The believer does not lie under the same obligation in the case of a union with an unbeliever, as in the case of one with a believer. In the former case he is not bound not to separate, if the unbeliever separate or "depart," in the latter nothing but "fornication" justifies separation [Photius in Æcumenius].

but God hath called us to peace--Our Christian calling is one that tends to "peace" (Ro 12:18), not quarrelling; therefore the believer should not ordinarily depart from the unbelieving consort (1Co 7:12-14), on the one hand; and on the other, in the exceptional case of the unbeliever desiring to depart, the believer is not bound to force the other party to stay in a state of continual discord (Mt 5:32). Better still it would be not to enter into such unequal alliances at all (1Co 7:40; 2Co 6:14).